津波サージ力による1自由度系の弾性応答

Abstract

Experiments using a reservoir discharge type flume with an orifice are conducted to investigate the dynamic characteristics of finite width wall structures attached to a flexible cantilever support subjected to surge forces. The surge acts as a step-like force with finite rise time in which the response is governed by the structure's vibrational properties. A structure vibrating under a single mode can be modeled as a single-degree-of-freedom(SDOF) system. When the structure is subjected to a surge, parts of its surface are submerged in water, giving rise to added intertial and hydrodynamic damping forces, which can be expressed as added masses and hydrodynamic damping coefficients. The focus of this research is to investigate and model the added mass and hydrodynamic damping coefficient for wall like structures subjected to surge forces. From potential theory, the added mass depends on the water density, inundation height, width of the structure, and their ratio. Assuming that the hydrodynamic damping has a form similar to aerodynamic damping, the hydrodynamic damping coefficient depends on the water density, water velocity, inundation height, width of the structure, and the ratio between inundation height and width of the structure. In order to investigate the added mass and hydrodynamic damping coefficient, finite width walls mounted on a flexible support are selected as the structural system. Three different materials and two different widths are selected as parameters for the wall. The first fundamental mode is translational in the direction of the flume. Two types of experiments are conducted. One in which the added mass and hydrodynamic damping coefficient is extracted from the system submerged in various inundation depths of still water, and the other in which they are extracted from the system subjected to surges resulting from 4 different initial reservoir heights. The former is conducted to obtain the ideal properties of the system when both sides of the plate are submerged in water as opposed to the latter which is to obtain actual properties of the system when only a single side is submerged. The time history of the measured response shear force of the structural system is decomposed into the quasi-static average force corresponding to the applied surge force and the oscillating dynamic force corresponding to the vibration of the structure, from which the added mass and hydrodynamic damping coefficient is obtained. From the stillwater experiments, a monotonic increase in added mass with respect to an increase in inundation depth was observed. By incorporating the mode of vibration and reduction of added mass due to the free water surface, the added mass can be modeled using the wall width, inundation height, and aspect ratio. From the surge experiments, a positive correlation between the added mass and inundation height is also observed, from which an added mass model similar to that for the stillwater case can be developed. The relationship between the total damping coefficient (material damping coeff. + hydrodynamic damping coeff.) and inundation depth obtained is dispersed but has a trend similar to the hydrodynamic damping model based on aerodynamic damping. Time history analysis is conducted, using the surge force, inundation height, and velocity time histories obtained from the experiments as input into the SDOF system with proposed added mass and hydrodynamic damping models. By using the proposed model, the decrease in fundamental frequency as well as the increase in damping observed in the experiments is adequately modeled. Though the damping is slightly overestimated for surges with smaller initial reservoir heights.